Question:where can I find explicit presentations of the group $Sp(n, \mathbb Z)$, for small $n$?

It is known that $Sp(n, \mathbb Z)$ admits a $2$-cocycle $h$ with values in $\mathbb Z/2\mathbb Z$ which I'd like to view in the following way. If we fix a presentation with relations forming a set $R$, then $h$ is a function $R \to \mathbb Z/2\mathbb Z$ (which fulfils some condition).

Question:where can I find an explicit description of this cocycle, in the form of what values does it take on elements of some presentation?